ON THE INTERPRETATION OF CLUSTERING FROM THE ANGULAR APM GALAXY SURVEY

We analyze the uncertainties in the amplitudes of the spatial correlat ion functions estimated from angular correlations in a sample from the Automatic Plate Measuring Facility (APM) Galaxy Survey, with b(J) = 1 7-20. We model the uncertainties in the selection function and in the evolution of clustering. In particular, we estimate sigma(8)(APM), the rms galaxy number fluctuation in spheres of radius at 8 h(-1) Mpc, fr om the measured angular variance in the APM. The uncertainty in sigma( 8)(APM) has three main contributions: 8% from sampling and selection f unction uncertainties, 7% from the uncertainty in the evolution of clu stering, and 3% from the uncertainty in the value of Omega(0). Includi ng all these contributions, we find that sigma(8)(APM) is in the range 0.78-1.08. If the galaxy clustering in the APM evolves as expected fr om gravitational clustering of matter fluctuations, then sigma(8)(APM) = 0.95 +/- 0.07 (1.00 +/- 0.08) for Omega(0) similar or equal to 1 (O mega(0) similar or equal to 0), close to the values for nearby optical samples. On the other hand, if we assume that clustering evolution is fixed in comoving coordinates, then sigma(8)(APM) = 0.83 +/- 0.05 (0. 87 +/- 0.06), closer to the results for nearby IRAS samples. The final uncertainty in the range of values for the hierarchical amplitudes S- J <(xi)over bar>(J)/<(xi)over bar>(2)J-1 is typically twice the estima ted sampling errors, with the highest values for the case of less clus tering evolution. We compare our estimates with other results and disc uss the implications for models of structure formation.